180 Mr. F. Baily on the Circular Micrometer. 



When an observation is to be made with this micrometer, let 

 the telescope be directed towards the object (a new planet, a 

 comet, or other small body) which may be made to describe 

 any chord of the inner circle ; and note the time of its ingress 

 at p, and its egress at p' : let us represent the former by t, and 

 the latter by t'. The telescope remaining perfectly steady, 

 note also the ingress and egress of any known star, contiguous 

 thereto, at s and s' : and represent the respective times, as 

 shown by the clock, by and 0'. Then will 



— and — 



be the respective times of the transit of the planet and the 

 known star at // and k, or at the horary circle N S. Con- 

 sequently the difference in the right ascension of these two 

 bodies will be 



dM=?±L-±±l- (A). 



The method of determining the difference of declination is 

 somewhat more complex. 



It is evident that the semi-chord ph = -^-^.15. cos A': and 



that the semi-chord sic = -— — .15. cos A: A being the de- 

 clination of the known star, and A' the estimated declination 

 of the small planet or comet. Make 



sin x = — == — —. (0'— 0). cos A 

 sm x = — = . (t — t). cos A 



r r v 



then we shall have 



Ck= r cos x = the dist. of k from the centre C 

 C/i = r cos .r'= the dist. of// from the centre C 



whence we obtain the difference of declination 



dD = ?(cos.r — cos^') (B) 



These computations are founded on the supposition that 

 the known star and the comet both pass through the circle, 

 on the same side of the centre C : that the known star is si- 

 tuated to the northward of the comet; and that it passes 

 through the circle after the comet. But it is easy to apply 

 the same principles to any other relative position of the bodies 

 observed : since it is only necessary to attend to the signs of 

 the respective quantities. Sufficient has been here stated to 

 point out the general mode of computation in such cases. 

 The reader who is desirous of pursuing this subject more at 



length 



